The strategy of using a change of variables to reduce to matrices of a special form has been used before in two dimensions
to prove solvability of Dirichlet and Regularity boundary value problems. The paper [1]} considered the \(L^p\)  Dirichlet problem for operators whose matrix
\(A(x,t) = A(x)\)  is \(t\) -independent and non-symmetric. The crucial observation that was used to
resolve the obstacles in solving this problem for some, possibly large, value of \(p\)  was the
discovery of a change of variables reducing matters to matrices of the form \(\begin{bmatrix} 1 &\gamma (x)\\0& \delta (x)\end{bmatrix}\) . For these
matrices, the proof of solvability used arguments that took advantage of the upper triangular structure. This particular
change of variable does not apply to the situation in Theorem REF  as it relied heavily on the \(t\) -independence.
